PreprintThe Pachner graph of 2spheresBenjamin A. Burton, Basudeb Datta and Jonathan SpreerAbstractIt is wellknown that the Pachner graph of nvertex triangulated 2spheres is connected, i.e., each pair of nvertex triangulated 2spheres can be turned into each other by a sequence of edge flips for each \(n\ge 4\). In this article, we study various induced subgraphs of this graph. In particular, we prove that the subgraph of \(n\)vertex flag 2spheres distinct from the double cone is still connected. In contrast, we show that the subgraph of nvertex stacked 2spheres has at least as many connected components as there are trees on \(\lfloor\frac{n5}{3}\rfloor\) nodes with maximum nodedegree at most four. AMS Subject Classification: Primary 57Q15; secondary 57M20, 05C10.
This paper is available as a pdf (780kB) file. It is also on the arXiv: arxiv.org/abs/1701.05144.
